Question

How do you find the multiplicative inverse of $\dfrac{5}{7}$?

Answer 1

Hint: In order to find the multiplicative inverse of $\dfrac{5}{7}$ we will recall the definition of multiplicative inverse. If a product of two numbers is 1 then these numbers are called multiplicative inverse. By using this definition we get the desired answer.

Complete step-by-step solution:
We have to find the multiplicative inverse of $\dfrac{5}{7}$.
We know that two numbers are called multiplicative inverses when their product is equal to 1. The inverse property of multiplication also states that if you multiply a number by its reciprocal the number is multiplicative inverse and the product is equal to 1.
So, let us assume that the multiplicative inverse of $\dfrac{5}{7}$ is $b$. Then we will get
$\Rightarrow \dfrac{5}{7}\times b=1$
On simplifying the above obtained equation we will get
\[\Rightarrow b=\dfrac{1}{\dfrac{5}{7}}\]
Now, to divide a fraction we need to flip the numerator and denominator of the second number. So, on simplifying further the above obtained equation we will get
\[\Rightarrow b=\dfrac{7}{5}\]
So the multiplicative inverse of $\dfrac{5}{7}$ is\[\dfrac{7}{5}\].

Note: When the product of two numbers is equal to one then the numbers are multiplicative inverses and 1 is known as the multiplicative identity. The multiplicative inverse of a number is also called the reciprocal of that number. When we have to find the multiplicative inverse of a fraction we can directly reciprocate the number. We need to change the numerator to denominator and vice-versa.